Abstract:
Data points of input data are processed by first determining a Laplacian matrix for the data. A spectrum of the Laplacian matrix includes an attractive spectrum of positive eigenvalues, a repulsive spectrum of negative eigenvalues, and a neutral spectrum of zero eigenvalues. An operation for the processing is determined using the Laplacian matrix, using information about the attractive spectrum, the repulsive spectrum, and the neutral spectrum, wherein the information includes the spectra and properties derived from the Spectra. Then, the operation is performed to produce processed data.
Abstract:
A controller for controlling a system includes a non-transitory computer-readable memory storing data for an operation and a control of the system and at least one processor operatively connected to the memory for determining a control signal transitioning a state of the system from a current state to a next state. At least two instances of the data are stored in the memory with different precisions defined by numbers of bits storing the instance in the memory. The processor determines the control signal using the instances of the data with the different precisions.
Abstract:
A method for a continuation model predictive control (CMPC) of a system determines at least a part of a preconditioner using an approximate coefficient function and determines a solution vector by solving a matrix equation of the CMPC with a coefficient matrix defined by an exact coefficient function at a current time step of a control using an iterative method with the preconditioner. The approximate coefficient function applied to a vector approximates a result of an application of the exact coefficient function to the vector. A control signal for controlling the system is generated using the solution vector.
Abstract:
A method determines a defect on a surface of an object. A symmetric representation of at least part of the object is generated and a pair of unmatched areas between the surface of the object and a surface of the symmetric representation is determined. Next, the defect on the surface of the object is determined based on the pair of unmatched areas.
Abstract:
A model predictive control (MPC) system for controlling an operation of a machine according to a model of the machine dynamics optimizes a cost function over a time-horizon subject to constraints to produce a sequence of control inputs to control the state of the machine over the time horizon. The machine is control using the first control input in the sequence. The cost function includes a first term defined by an objective of the MPC and a second term penalizing deviation of a state of the machine from a value satisfying an equation of dynamics of the machine.
Abstract:
A method for a continuation model predictive control (CMPC) of a system determines at least a part of a preconditioner using an approximate coefficient function and determines a solution vector by solving a matrix equation of the CMPC with a coefficient matrix defined by an exact coefficient function at a current time step of a control using an iterative method with the preconditioner. The approximate coefficient function applied to a vector approximates a result of an application of the exact coefficient function to the vector. A control signal for controlling the system is generated using the solution vector.
Abstract:
A method reconstructs a signal by sampling the signal using a sampling procedure to obtain an input signal. A consistent set is determined from the input signal including the first elements such that applying the sampling procedure to the first elements results in the input signal. According to the type of the signal, a guiding set is determined including second elements disjoint from the first elements. A reconstruction set including third elements is generated so that the third elements minimize a sum of a first similarity measure of the third elements to the second elements and a second similarity measure of the third elements to the first elements. A transformed signal that minimizes a function on the reconstruction set is determined. A reconstructed signal is rendered so that a third similarity measure of the reconstructed signal to the transformed signal is smaller than a tolerance.
Abstract:
A controller for controlling a system includes a non-transitory computer-readable memory storing data for an operation and a control of the system and at least one processor operatively connected to the memory for determining a control signal transitioning a state of the system from a current state to a next state. At least two instances of the data are stored in the memory with different precisions defined by numbers of bits storing the instance in the memory. The processor determines the control signal using the instances of the data with the different precisions.
Abstract:
A method reconstructs a signal by sampling the signal using a sampling procedure to obtain an input signal. A consistent set is determined from the input signal including the first elements such that applying the sampling procedure to the first elements results in the input signal. According to the type of the signal, a guiding set is determined including second elements disjoint from the first elements. A reconstruction set including third elements is generated so that the third elements minimize a sum of a first similarity measure of the third elements to the second elements and a second similarity measure of the third elements to the first elements. A transformed signal that minimizes a function on the reconstruction set is determined. A reconstructed signal is rendered so that a third similarity measure of the reconstructed signal to the transformed signal is smaller than a tolerance.
Abstract:
A method modulates data for optical communication by first encoding the data using a forward error correction (FEC) encoder to produce encoded data, which are encoded using a block encoder to produce block encoded data such that Hamming distances between code words that represent the block encoded data are increased. The block encoded data are mapped to produce mapped data such that Euclidian distances between the constellation points are increased. Then, the mapped data are modulated in a transmitter to a modulated signal for an optical channel.